1.5 Mass conservation performance
1.5.1 Simulation class: DO
This is the simplest simulation class and it has oxygen as the only mandatory model class. For illustrative purposes, the optional pathogens model class has also been included in this mass balance simulation. The computed variables presented are therefore:
- Dissolved oxygen
- Pathogen 1 (which includes attachment dynamics)
- Pathogen 2 (which excludes attachment dynamics)
The initial conditions are:
- Dissolved oxygen: 8.0 mg/L
- Pathogen 1 alive, attached and dead: 1e6 CFU/100mL, 1e5 CFU/100mL, 1e5 CFU/100mL
- Pathogen 2 alive and dead: 1e5 CFU/100mL, 1e4 CFU/100mL
The relevant fluxes considered are (coloured as
- Dissolved oxygen
Sediment - Atmospheric (both source and sink)
- Pathogen 1
Natural mortality Inactivation due to irradiance - Attachment and detachment
Settling
- Pathogen 2
Natural mortality Inactivation due to irradiance Settling
The mass conservation performance of the WQ Module for dissolved oxygen and summed pathogens (i.e. pathogen 1 and pathogen 2 combined) is presented in Figure 1.2, via \(DO_{mb}\), \(PTHa_{mb}\) and \(PTHd_{mb}\). Over the duration of the simulation, mass conservation holds to within 0.02%. It is noted that the alive pathogens mass balance (\(PTHa_{mb}\)) is truncated at 2 weeks because alive concentrations are six orders of magnitude lower that initial conditions by this time, and this pushes mass balance percentage error calculations to approach a divide by zero. Dead pathogen mass conservation is less affected because overall changes are approximately one order of magnitude only. Relevant fluxes used to compute this mass conservation, as well as total pathogen mass conservation, are presented subsequently.
Figure 1.2: Dissolved oxygen mass conservation parameters \(DO_{mb}(t)\), \(PTHa_{mb}(t)\) and \(PTHd_{mb}(t)\)
Figure 1.3: Dissolved oxygen WQ Module fluxes \(F_i(t)\) used to compute \(DO_{mp}(t)\)
The following are pathogen fluxes. Because fluxes vary by several orders of magnitude, they are presented as logarithms, as -log\(_{10}\)(-flux). For example, a plotted value of -15 below, means that the actual flux was -1e15 CFU/15 minutes (not 1e-15 CFU/15 minutes), and a change in value from -16 to -15 represents a tenfold decrease in flux.
Figure 1.4: Pathogen WQ Module fluxes \(F_i(t)\) used to compute \(PTHa_{mp}(t)\) and \(PTHd_{mp}(t)\)
Figure 1.5: Total pathogen mass conservation parameter \(PTHT_{mb}(t)\)
Following are the WQ Module control file commands used to generate the above.
1.5.2 Simulation class: Inorganics
The computed variables presented are:
- Dissolved oxygen
- Silicate
- Ammonium
- Nitrate
- FRP
- Adsorbed FRP
- Two phytoplankton groups (one each for the basic and advanced model)
Pathogen behaviour is unchanged from the DO simulation class mass balance model presented in Section 1.5.1 so the corresponding mass balance is omitted for clarity.
The initial conditions are:
- Dissolved oxygen: 8.0 mg/L
- Silicate: 50.0 mg/L
- Ammonium: 0.15 mg/L
- Nitrate: 0.2 mg/L
- FRP: 0.04 mg/L
- Adsorbed FRP: 0.02 mg/L
- Blue green phytoplankton: 2.0 \(\mu\)g/L (advanced model)
- Blue green internal nitrogen: 0.008 mg/L
- Blue green internal phosphorus: 0.0012 mg/L
- Green phytoplankton: 5.0 \(\mu\)g/L (basic model)
The relevant fluxes considered are:
- Dissolved oxygen
Sediment - Atmospheric (both source and sink)
Nitrification Phytoplankton primary productivity Phytoplankton respiration
- Silicate
Sediment Phytoplankton primary productivity Phytoplankton mortality Phytoplankton excretion
- Ammonium
Sediment Atmospheric (wet and dry deposition) Nitrification Anaerobic oxidation of ammonium Dissimilatory reduction of nitrate to ammonium Phytoplankton primary productivity Phytoplankton mortality Phytoplankton excretion
- Nitrate
Sediment Atmospheric (wet and dry deposition)Nitrification Denitrification Anaerobic oxidation of ammonium Dissimilatory reduction of nitrate to ammonium Phytoplankton primary productivity
- FRP
Sediment Atmospheric Adsorption anddesorption Phytoplankton primary productivity Phytoplankton mortality Phytoplankton excretion
- FRP Adsorbed
Adsorption anddesorption
- Phytoplankton (both groups)
Phytoplankton primary productivity Phytoplankton respiration Phytoplankton mortality Phytoplankton excretion Phytoplankton sedimentation
The mass conservation performance of the WQ Module is presented in Figure 1.6, via \(DO_{mb}(t)\), \(Si_{mb}(t)\), \(Amm_{mb}(t)\), \(Nit_{mb}(t)\), \((FRP+FRPAds)_{mb}(t)\) and \(PHY_{mb}(t)\). Over the duration of the simulation, mass conservation holds to within approximately 0.014%. Relevant fluxes used to compute these mass conservations, as well as total nitrogen and total phosphorus mass conservations, are presented subsequently.
Figure 1.6: Inorganics mass conservation parameters \(DO_{mb}(t)\), \(Si_{mb}(t)\), \(Amm_{mb}(t)\), \(Nit_{mb}(t)\), \(FRP_{mb}(t)\) and \(PHY_{mb}(t)\)
Figure 1.7: Dissolved oxygen WQ Module fluxes \(F_i(t)\) used to compute \(DO_{mb}(t)\)
Figure 1.8: Silicate WQ Module fluxes \(F_i(t)\) used to compute \(Si_{mb}(t)\)
Figure 1.9: Ammonium WQ Module fluxes \(F_i(t)\) used to compute \(Amm_{mb}(t)\)
Ammonium anammox fluxes are zero in the dissolved oxygen conditions of this mass conservation model.
Figure 1.10: Nitrate WQ Module fluxes \(F_i(t)\) used to compute \(Nit_{mb}(t)\)
Nitrate anammox fluxes are zero in the dissolved oxygen conditions of this mass conservation model.
Figure 1.11: FRP + FRPAds WQ Module fluxes \(F_i(t)\) used to compute \((FRP+FRPAds)_{mb}(t)\)
Figure 1.12: Phytoplankton WQ Module fluxes \(F_i(t)\) used to compute \(PHY_{mb}(t)\)
Figure 1.13: Inorganics total nitrogen and total phosphorus mass conservation parameters \(TN_{mb}(t)\) and \(TP_{mb}(t)\)
Following are the WQ Module control file commands used to generate the above.
1.5.3 Simulation class: Organics
The computed variables presented are:
- Dissolved oxygen
- Silicate
- Ammonium
- Nitrate
- FRP
- Adsorbed FRP
- Particulate organic carbon
- Dissolved organic carbon
- Particulate organic nitrogen
- Dissolved organic nitrogen
- Particulate organic phosphorus
- Dissolved organic phosphorus
- Refractory particulate organic matter
- Refractory dissolved organic carbon
- Refractory dissolved organic nitrogen
- Refractory dissolved organic phosphorus
- Two phytoplankton groups (one each for the basic and advanced model)
Again, pathogen behaviour is unchanged from the DO simulation class mass balance model presented in Section 1.5.1 so the corresponding mass balance is omitted for clarity.
The initial conditions are:
- Dissolved oxygen: 8.0 mg/L
- Silicate: 1.0 mg/L
- Ammonium: 0.15 mg/L
- Nitrate: 0.2 mg/L
- FRP: 0.04 mg/L
- Adsorbed FRP: 0.02 mg/L
- Particulate organic carbon: 2.5 mg/L
- Dissolved organic carbon: 1.5 mg/L
- Particulate organic nitrogen: 0.3 mg/L
- Dissolved organic nitrogen: 0.1 mg/L
- Particulate organic phosphorus: 0.06 mg/L
- Dissolved organic phosphorus: 0.03 mg/L
- Refractory particulate organic matter: 2.1 mg/L
- Refractory dissolved organic carbon: 1.6 mg/L
- Refractory dissolved organic nitrogen: 0.6 mg/L
- Refractory dissolved organic phosphorus: 0.04 mg/L
- Blue green phytoplankton: 2.0 \(\mu\)g/L (advanced model)
- Blue green internal nitrogen: 0.008 mg/L
- Blue green internal phosphorus: 0.0012 mg/L
- Green phytoplankton: 5.0 \(\mu\)g/L (basic model)
The relevant fluxes considered are:
- Dissolved oxygen
Sediment - Atmospheric (both source and sink)
Nitrification Dissolved organic carbon mineralisation (oxygen based) Phytoplankton primary productivity Phytoplankton respiration
- Silicate
Sediment Phytoplankton primary productivity Phytoplankton mortality Phytoplankton excretion
- Ammonium
Sediment Atmospheric (wet and dry deposition) Nitrification Anaerobic oxidation of ammonium Dissimilatory reduction of nitrate to ammonium Dissolved organic nitrogen mineralisation Dissolved refractory organic matter photolysis Phytoplankton primary productivity
- Nitrate
Sediment Atmospheric (wet and dry deposition) Nitrification Denitrification Anaerobic oxidation of ammonium Dissimilatory reduction of nitrate to ammonium Dissolved organic carbon mineralisation (nitrate based) Phytoplankton primary productivity flux
- FRP
Sediment Atmospheric Adsorption anddesorption Dissolved organic phosphorus mineralisation Dissolved refractory organic matter photolysis Phytoplankton primary productivity
- FRP Adsorbed
Adsorption anddesorption
- Particulate organic carbon, nitrogen and phosphorus
Hydrolysis Breakdown of refractory particulate organic matter Phytoplankton mortality
- Dissolved organic carbon, nitrogen and phosphorus
Sediment Hydrolysis Mineralisation Dissolved refractory organic matter photolysis Dissolved refractory organic matter activation Phytoplankton excretion
- Refractory particulate organic matter
Breakdown
- Refractory organic carbon, nitrogen and phosphorus
Dissolved refractory organic matter photolysis Dissolved refractory organic matter activation
- Phytoplankton (both groups)
Phytoplankton primary productivity Phytoplankton respiration Phytoplankton mortality Phytoplankton excretion Phytoplankton sedimentation
The mass conservation performance of the WQ Module is presented in Figure 1.14, via \(DO_{mb}(t)\), \(Si_{mb}(t)\), \(Amm_{mb}(t)\), \(Nit_{mb}(t)\), \((FRP+FRPAds)_{mb}(t)\), \(POC_{mb}(t)\), \(DOC_{mb}(t)\), \(PON_{mb}(t)\), \(DON_{mb}(t)\), \(POP_{mb}(t)\), \(DOP_{mb}(t)\), \(RPOM_{mb}(t)\), \(RDOC_{mb}(t)\), \(RDON_{mb}(t)\), \(RDOP_{mb}(t)\) and \(PHY_{mb}(t)\). Over the duration of the simulation, mass conservation holds to within 0.024%. Relevant fluxes used to compute these mass conservations, as well as total nitrogen and total phosphorus mass conservations, are presented subsequently.
Figure 1.14: Organics mass conservation parameters \(DO_{mb}(t)\), \(Si_{mb}(t)\), \(Amm_{mb}(t)\), \(Nit_{mb}(t)\), \(FRP_{mb}(t)\), \(POC_{mb}(t)\), \(DOC_{mb}(t)\), \(PON_{mb}(t)\), \(DON_{mb}(t)\), \(POP_{mb}(t)\), \(DOP_{mb}(t)\), \(RPOM_{mb}(t)\), \(RDOC_{mb}(t)\), \(RDON_{mb}(t)\), \(RDOP_{mb}(t)\) and \(PHY_{mb}(t)\)
Figure 1.15: Dissolved oxygen WQ Module fluxes \(F_i(t)\) used to compute \(DO_{mb}(t)\)
Figure 1.16: Silicate WQ Module fluxes \(F_i(t)\) used to compute \(Si_{mb}(t)\)
Figure 1.17: Ammonium WQ Module fluxes \(F_i(t)\) used to compute \(Amm_{mb}(t)\)
Ammonium anammox fluxes are zero in the dissolved oxygen conditions of this mass conservation model.
Figure 1.18: Nitrate WQ Module fluxes \(F_i(t)\) used to compute \(Nit_{mb}(t)\)
Nitrate anammox fluxes are zero in the dissolved oxygen conditions of this mass conservation model.
Figure 1.19: FRP+FRPAds WQ Module fluxes \(F_i(t)\) used to compute \((FRP+FRPAds)_{mb}(t)\)
Figure 1.20: POC WQ Module fluxes \(F_i(t)\) used to compute \(POC_{mb}(t)\)
Figure 1.21: DOC WQ Module fluxes \(F_i(t)\) used to compute \(DOC_{mb}(t)\)
Figure 1.22: PON WQ Module fluxes \(F_i(t)\) used to compute \(PON_{mb}(t)\)
Figure 1.23: DON WQ Module fluxes \(F_i(t)\) used to compute \(DON_{mb}(t)\)
Figure 1.24: POP WQ Module fluxes \(F_i(t)\) used to compute \(POP_{mb}(t)\)
Figure 1.25: DOP WQ Module fluxes \(F_i(t)\) used to compute \(DOP_{mb}(t)\)
Figure 1.26: RPOM WQ Module fluxes \(F_i(t)\) used to compute \(RPOM_{mb}(t)\)
Figure 1.27: RDOC WQ Module fluxes \(F_i(t)\) used to compute \(RDOC_{mb}(t)\)
Figure 1.28: RDON WQ Module fluxes \(F_i(t)\) used to compute \(RDON_{mb}(t)\)
Figure 1.29: RDOP WQ Module fluxes \(F_i(t)\) used to compute \(RDOP_{mb}(t)\)
Figure 1.30: Phytoplankton WQ Module fluxes \(F_i(t)\) used to compute \(PHY_{mb}(t)\)
Figure 1.31: Organics total nitrogen and total phosphorus mass conservation parameters \(TN_{mb}(t)\) and \(TP_{mb}(t)\)
Following are the WQ Module control file commands used to generate the above.